Mesure de champs cinématiques particulaires haute définition dans les milieux granulaires bidimensionnels G. Combe, V. Richefeu Présenté par O. Jenck

2 Schneebeli** rods : a 2D granular material 2D Grains ≡ 6 cm long cylinders of various sections and different diameters **G. Schneebeli, CRAS, 243(1): (1956) ϕ = [1,5 - 2,5 - 3,5 mm] ϕ = [ mm] PVC rodsWood rods Mixtures of discs and rectangles Hexagonal shapes

wooden rods in 1γ2ε shear device

**H.A. Joer & al, Géotechnique, 48(5): (1996) 1 γ 2 ε ** Shear apparatus 4 Possible tests Oedometric compression Biaxial test: vertical compression, lateral stress constant Simple shear test: tilt with constant vertical stress Isotropic compression Test with imposed rotation of the principal axes of STRAINS or STRESSES (more complex) And

**H.A. Joer & al, Géotechnique, 48(5): (1996) 1 γ 2 ε ** Shear apparatus 5 What do we measure ? - Macroscopic level (sample scale): Lengths and tilt of the boundaries ➟ Strain macroscopic tensor Forces at the corners of the frame ➟ Stress macroscopic tensor - Microscopic level (grain scale): Position and orientation of grains ➟ full grain kinematics ➟ Contacts list

pictures MPixels Shear test on 2000 wooden rods Assessing kinematics using “modern” Digital Camera (2010 ➟...) movie picture speed x 500

7 PIT : Digital Image Correlation technique adapted to track “automatically” full kinematics of rigid bodies PIT : Particle Image Tracking Combe & Richefeu, Powders and Grains 2013 Rigid-motion relation to track u, v and θ… … with a subpixel resolution using bilinear, bicubic or biquintic interpolation Tracker PIT software

8 PIT: Particle Image Tracking Combe & Richefeu, Powders and Grains 2013 Correlation works between the first and the current images (thanks to rigid motion and ZNCC) ➡ digital truncation errors are NOT cumulated. A rescue procedure that basically increase the search zone and avoid exclusion zones of well-found bodies. Increased search zone Well-found bodies Exclusion zone Body being « rescued »

Accuracy with synthetic images (from Orteu et al., 2006) 9 PIT: Particle Image Tracking Combe & Richefeu, Powders and Grains 2013 ➠ Same intrinsic accuracy as the codes used in the GdR CNRS 2519 Courtesy, L. Robert

Accuracy with real images that involve the whole measurement chain. Solid motion = distance and angle conservation 10 PIT : Particle Image Tracking Combe & Richefeu, Powders and Grains 2013 Correction of distortion drastically improve the accuracy.

Quasi-Static shear test 11 An experimental study inspired from the numerical work of Radjaï & Roux, PRL (2002) Fluctuations of displacement Richefeu & al., Géotech. Lett., 2, ,(2012)

Quasi-Static shear test 12 An experimental study inspired from the numerical work of Radjaï & Roux, PRL (2002) Fluctuations of displacement Richefeu & al., Géotech. Lett., 2, ,(2012) Stream lines

13 Richefeu & al., Géotech. Lett., 2, ,(2012) Fluctuations of displacement Fluctuations are due to geometrical constraints

➠ Statistical analysis of the fluctuation of displacement 14 Richefeu & al., Géotech. Lett., 2, ,(2012) Fluctuations of displacement **C. Tsallis, Journal of Statistical Physics 52, 479–487 (1988) **

15 Richefeu & al., Géotech. Lett., 2, ,(2012) Fluctuations of displacement Small shear-strain increment Large shear-strain increment

16 small Δγ ➠ long range correlation large Δγ ➠ short range correlation 10 vortice-like structures Vortex Richefeu & al., Géotech. Lett., 2, ,(2012) Fluctuations of displacement

Conclusions An digital image correlation tool has been developed with a special concern with “particle tracking”. It has been shown to be as accurate as other tools used in the field of continuous materials. On a direct 2D shear test, the displacement fluctuations was defined as the measured displacements subtracted by the displacements interpolated from the boundary movements (affine field). Some specific features of the fluctuations, that play a role analogue to the dislocations in steel plasticity, have been characterized. And now… we work on how to derive a plastic model of granular material from the fluctuations of grain displacements.

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